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First- and Second-Order Optimality Conditions for Optimal Control Problems of State Constrained Integral Equations

Author

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  • J. Frédéric Bonnans

    (Ecole Polytechnique)

  • Constanza Vega

    (UBA)

  • Xavier Dupuis

    (Ecole Polytechnique)

Abstract

This paper deals with optimal control problems of integral equations, with initial–final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with constraints of arbitrary high orders. First-order necessary conditions of optimality are given by the description of the set of Lagrange multipliers. Second-order necessary conditions are expressed by the nonnegativity of the supremum of some quadratic forms. Second-order sufficient conditions are also obtained in the case where these quadratic forms are of Legendre type.

Suggested Citation

  • J. Frédéric Bonnans & Constanza Vega & Xavier Dupuis, 2013. "First- and Second-Order Optimality Conditions for Optimal Control Problems of State Constrained Integral Equations," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 1-40, October.
    • Handle: RePEc:spr:joptap:v:159:y:2013:i:1:d:10.1007_s10957-013-0299-3
    DOI: 10.1007/s10957-013-0299-3
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    References listed on IDEAS

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    1. C. De La Vega, 2006. "Necessary Conditions for Optimal Terminal Time Control Problems Governed by a Volterra Integral Equation," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 79-93, July.
    2. M. I. Kamien & E. Muller, 1976. "Optimal Control with Integral State Equations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(3), pages 469-473.
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    Cited by:

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    2. Tang, Xiaojun, 2015. "Efficient Chebyshev collocation methods for solving optimal control problems governed by Volterra integral equations," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 118-128.

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